Phasor Time-Domain Power System Modeling and …vanfrl/documents/mscthesis/2015...ditionally, dynamic modeling and simulation of power systems is performed by using di erent and mostly

DEGREE PROJECT, IN ,SMART ELECTRICAL NETWORKS AND SYSTEMSSECOND LEVEL

STOCKHOLM, SWEDEN 2015

Phasor Time-Domain Power SystemModeling and Simulation using theStandardized Modelica Language:Conventional and PowerElectronic-Based Devices

MOHAMMED AHSAN ADIB MURAD

KTH ROYAL INSTITUTE OF TECHNOLOGY

ELECTRICAL ENGINEERING

Phasor Time-Domain Power System Modeling and

Simulation using the Standardized Modelica

Language: Conventional and Power Electronic-Based

Devices

Mohammed Ahsan Adib Murad

Supervisor and Examiner: Prof.Dr.-Ing. Luigi Vanfretti, KTH.

Supervisor: Francisco Gomez, KTH.

Electric Power Systems Dept.

Royal Institute of Technology (KTH)

December 2014

i

Abstract

Modern electric power systems are complex networks that ensure continuous supply of

electricity. For the planning and operation of these complex networks, modeling and sim-

ulations are essential to satisfy operational requirements or planning constraints. Tra-

ditionally, dynamic modeling and simulation of power systems is performed by using

different and mostly incompatible software packages. This issue is currently being ad-

dressed through the Common Information Model (CIM) for power system applications,

however, there are still many challenges for Power system dynamic modeling and simu-

lation without any ambiguity.

To overcome these challenges, this thesis develops unambiguous models for consistent

model exchange, which are compatible in different simulation environments that sup-

port the Modelica language. Modelica, an object-oriented equation-based standardized

language, is proposed as possible solution to these challenges as it can represent and

exchange dynamic models with a strict mathematical description.

In this thesis, modeling and simulation of controllable power electronic-based com-

ponents and conventional components for phasor time-domain simulation is carried out

using Modelica. The work in this thesis contributes to a Modelica power systems library

being developed by KTH SmartTS Lab under the FP7 iTesla project and other projects

supported by Statnett SF. Both software implementation in Modelica of each component,

and software-to-software validation against PSAT is carried out.

ii

iii

Sammanfattning

Moderna elkraftsystem r komplexa ntverk som skerstller en kontinuerlig tillfrsel av elkraft.

Fr att kunna uppfylla de tekniska krav och begrnsningar som stlls vid planering och drift

r modellering och simulering av dessa komplexa ntverk av avgrande betydelse. Vanligtvis

sker modellering och simulering av kraftsystemets dynamik i olika och oftast inkompat-

ibla programvaror. Detta problem sker Common Information Model (CIM) fr kraft-

systemkomponenter att lsa, men mnga hinder kvarstr innan dynamisk modellering och

simulering av kraftsystemet kan ske utan tvetydigheter.

Fr att lsa dessa utmaningar s utvecklar detta examensarbete entydiga modeller fr

ett konsekvent utbyte av modeller mellan simuleringsprogramvaror som stdjer modeller-

ingssprket Modelica. Modelica, ett standardiserat, objektorienterat och ekvationsbaserat

sprk, fresls som en mjlig lsning fr dessa utmaningar d det kan representera och utbyta

modeller genom en strikt matematisk beskrivning.

I detta examensarbete utfrs modellering och simulering i Modelica av bde styrbara

kraftelektronik och konventionella kraftsystemkomponenter fr tidssimulering med fasvek-

torer. Detta examensarbete bidrar till det Modelica bibliotek fr elkraftsystem som utveck-

las av KTH SmartTS Lab i FP7 projektet iTesla och andra projekt som stttas av Statnett

SF. Modellerna som utvecklas i Modelica valideras med hjlp av mjukvaru-validering med

PSAT som referens.

iv

v

Acknowledgement

I am grateful to Assoc. Prof. Dr.-Ing. Luigi Vanfretti for giving me the

opportunity as his master thesis student, he has been a great support during the whole

work. In addition, special gratitude and thank to my supervisor Francisco Gomez for

his generous help, warm encouragement and support.

I would like to thank my program coordinator, Assoc. Prof. Hans Edin, for his

guidance for the past two years of my master’s program. In addition, special thank to

EIT/KIC-InnoEnergy for funding my studies in Smart Electrical Network and Systems

(SENSE) program.

I would like to thank all the people who helped me and supported me during this

project and special thank to Apostolis Kristal, Md Jahidul Islam Razan, Le Qi, Yuwa

Choompoobutrgool, Wei Li, Jan Lavenius and all the members of the SmarTS Lab.

Without the help from the group members, the completion of this thesis would not have

been possible. Finally, I would like to thank my beloved family for their support, as well

as all of my friends.

vi

vii

Contents

List of Figures xiii

List of Tables xiv

1 Introduction 2

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Overview of the Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Modeling Languages 6

2.1 Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Modelica Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Modelica Simulation Environment . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Modelica Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Power System Analysis Toolbox (PSAT) . . . . . . . . . . . . . . . . . . 9

3 Power System Component Modeling 11

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Power System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.1 Connectors and Connection . . . . . . . . . . . . . . . . . . . . . 12

3.2.2 Modeling Methodology . . . . . . . . . . . . . . . . . . . . . . . . 13

viii

CONTENTS CONTENTS

3.3 FACTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3.1 Thyristor Controlled Series Compensator(TCSC) . . . . . . . . . 15

3.3.2 TCSC in Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.3 Static Synchronous Compensator(STATCOM) . . . . . . . . . . . 18

3.3.4 STATCOM in Modelica . . . . . . . . . . . . . . . . . . . . . . . 19

3.3.5 Static Synchronous Source Series Compensator(SSSC) . . . . . . 21

3.3.6 SSSC in Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.7 Unified Power Flow Controller(UPFC) . . . . . . . . . . . . . . . 24

3.3.8 UPFC in Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.4 Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.4.1 Three-Winding Transformer(TWT) . . . . . . . . . . . . . . . . . 26

3.4.2 TWT in Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.3 Under Load Tap Changer . . . . . . . . . . . . . . . . . . . . . . 28

3.4.4 ULTC in Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.4.5 Phase Shifting Transformer(PST) . . . . . . . . . . . . . . . . . . 31

3.4.6 PST in Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Power System Model Validation 35

4.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3 Validation of FACTS Devices . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.1 Validation of TCSC model . . . . . . . . . . . . . . . . . . . . . . 37

4.3.2 Simulation Result of TCSC validation . . . . . . . . . . . . . . . 37

4.3.3 Validation of STATCOM model . . . . . . . . . . . . . . . . . . . 40

4.3.4 Simulation Result of STATCOM . . . . . . . . . . . . . . . . . . 41

4.3.5 Validation of SSSC model . . . . . . . . . . . . . . . . . . . . . . 42

4.3.6 Validation of UPFC model . . . . . . . . . . . . . . . . . . . . . . 43

ix

4.4 Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.5 Transformer Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . 46

4.6 IEEE Standard Test System . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.6.1 IEEE 9-Bus Test System . . . . . . . . . . . . . . . . . . . . . . . 47

4.6.2 IEEE 14-Bus Test System . . . . . . . . . . . . . . . . . . . . . . 48

4.6.3 Quantitative Assessment . . . . . . . . . . . . . . . . . . . . . . . 50

4.6.4 Simulation Result of IEEE 9 and 14-Bus Test System . . . . . . 51

5 Discussion and Conclusion 53

5.1 Modelica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2 Modeling and validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6 Future Work 56

6.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

A Test System and Validation 57

A.1 Test System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.2 Software to Software Validation . . . . . . . . . . . . . . . . . . . . . . . 59

A.3 Test System Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.3.1 9 Bus Test System . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.3.2 14-Bus Test System . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Bibliography 69

x

List of Figures

1.1 Time frame of different power system dynamics. . . . . . . . . . . . . . . 3

2.1 Examples of Modelica Models [24]. . . . . . . . . . . . . . . . . . . . . . 6

2.2 Textual programming in Modelica. . . . . . . . . . . . . . . . . . . . . . 9

2.3 Graphical User Interface of PSAT. . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Connection diagram for components. . . . . . . . . . . . . . . . . . . . . 12

3.2 Schematic of electrical PwPin connector. . . . . . . . . . . . . . . . . . . 13

3.3 Connecting two components in Modelica. . . . . . . . . . . . . . . . . . . 13

3.4 Control block diagram of TCSC [27]. . . . . . . . . . . . . . . . . . . . . 15

3.5 Control block diagram of STATCOM [27]. . . . . . . . . . . . . . . . . . 19

3.6 STATCOM GUI based model in Modelica. . . . . . . . . . . . . . . . . . 19

3.7 Circuit diagram of SSSC [27]. . . . . . . . . . . . . . . . . . . . . . . . . 21

3.8 Control block diagram of SSSC [27]. . . . . . . . . . . . . . . . . . . . . . 22

3.9 Circuit diagram of UPFC [27]. . . . . . . . . . . . . . . . . . . . . . . . . 24

3.10 Control block diagram of UPFC [27]. . . . . . . . . . . . . . . . . . . . . 25

3.11 Equivalent circuit: Three-Winding Transformer [27]. . . . . . . . . . . . . 26

3.12 Three Winding Tansformer in Modelica. . . . . . . . . . . . . . . . . . . 28

3.13 Equivalent π circuit: Under Load Tap Changer [27]. . . . . . . . . . . . . 29

3.14 Secondary voltage control scheme of ULTC [27]. . . . . . . . . . . . . . . 29

xi

LIST OF FIGURES LIST OF FIGURES

3.15 Equivalent circuit of Phase Shifting Transformer [27]. . . . . . . . . . . . 32

3.16 Control scheme of Phase Shifting Transformer [27]. . . . . . . . . . . . . 32

4.1 Test Model of TCSC type: Reactance. . . . . . . . . . . . . . . . . . . . 38

4.2 Test Model of TCSC type: Alpha. . . . . . . . . . . . . . . . . . . . . . . 38

4.3 Software to software validation of TCSC Reactance Model. . . . . . . . . 39

4.4 Software to software validation of TCSC Alpha Model. . . . . . . . . . . 39

4.5 Test Model of STATCOM. . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.6 Software to software validation of STATCOM GUI based Model. . . . . . 42

4.7 Test Model of SSSC in PSAT. . . . . . . . . . . . . . . . . . . . . . . . . 42

4.8 Test Model of SSSC in Modelica. . . . . . . . . . . . . . . . . . . . . . . 43

4.9 Software to software validation of SSSC in constant power mode. . . . . . 43

4.10 Test Model of UPFC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.11 Software to software validation of UPFC in constant power mode. . . . . 44

4.12 Test Model of TWT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.13 Test Model of ULTC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.14 Test Model of PST. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.15 Software to software validation of ULTC. . . . . . . . . . . . . . . . . . . 47

4.16 IEEE 9-Bus Test system. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.17 IEEE 14-Bus Test system in PSAT with ULTC. . . . . . . . . . . . . . . 49

4.18 IEEE 14-Bus Test system in Modelica with ULTC. . . . . . . . . . . . . 50

4.19 Software to software validation results of IEEE 9-Bus with STATCOM. . 52

4.20 Software to software validation results of IEEE 14-Bus with ULTC. . . . 52

5.1 Comparison of different solvers of Open Modelica with Trapezoidal rule ofPSAT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2 Total simulation time spending for the solvers in Open Modelica withdifferent tolerance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

xii

A.1 IEEE 9-Bus Test system with TCSC Reactance Model (between Bus 8 andBus 9) in OpenModelica. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.2 IEEE 14-Bus Test system with PST (Between Bus 4 and Bus 9) in Modelica. 58

A.3 IEEE 14-Bus Test system with TWT in Modelica. . . . . . . . . . . . . . 58

A.4 Software to software validation of STATCOM Text based Model. . . . . . 59

A.5 Software to software validation of SSSC in constant voltage mode. . . . . 59

A.6 Software to software validation of TWT. . . . . . . . . . . . . . . . . . . 60

A.7 Software to software validation of PST. . . . . . . . . . . . . . . . . . . . 60

A.8 Software to software validation of IEEE 9-Bus system with TCSC. . . . . 61

A.9 Software to software validation of IEEE 9-Bus system with SSSC. . . . . 61

A.10 Software to software validation of IEEE 9-Bus system with UPFC. . . . . 62

A.11 Software to software validation of IEEE-14 Bus system with PST. . . . . 63

A.12 Software to software validation of IEEE 14-Bus system with TWT. . . . 63

A.13 WSCC 9-Bus test System [27]. . . . . . . . . . . . . . . . . . . . . . . . . 64

A.14 IEEE 14-Bus test System [27]. . . . . . . . . . . . . . . . . . . . . . . . . 66

xiii

List of Tables

2.1 Modelica based software environments. . . . . . . . . . . . . . . . . . . . 8

4.1 Simulation set up for the validation. . . . . . . . . . . . . . . . . . . . . . 35

4.2 Calculations using equation 4.1 . . . . . . . . . . . . . . . . . . . . . . . 51

A.1 Synchronous Generator Data . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.2 Line Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.3 Two winding transformer data . . . . . . . . . . . . . . . . . . . . . . . . 65

A.4 PQ Load data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.5 AVR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.6 Synchronous Generator Data of IEEE 14-Bus system . . . . . . . . . . . 66

A.7 Line Data of IEEE 14-Bus System . . . . . . . . . . . . . . . . . . . . . . 67

A.8 Two winding transformer data of IEEE-14 Bus system . . . . . . . . . . 67

A.9 PQ Load data of IEEE-14 Bus system . . . . . . . . . . . . . . . . . . . 67

A.10 AVR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.11 ULTC (in IEEE-14 Bus) data . . . . . . . . . . . . . . . . . . . . . . . . 68

A.12 PST (in IEEE-14 Bus) data . . . . . . . . . . . . . . . . . . . . . . . . . 68

A.13 TWT (in IEEE-14 Bus) data . . . . . . . . . . . . . . . . . . . . . . . . . 68

xiv

Notations

PSAT Power System Analysis Toolbox

EMT Electro-Magnetic Transient

DAE Differential and Algebraic Equation

GUI Graphical User Interface

ODE Ordinary Differential Equation

TCSC Thyristor Controlled Series Compensator

STATCOM Static Synchronous Compensator

SSSC Static Synchronous source Series Compensator

UPFC Unified Power Flow Controller

ULTC Under Load Tap Changer

PST Phase Shifting Transformer

TWT Three Winding Transformer

AVR Automatic Voltage Regulator

FACTS Flexible AC Transmission System

IEEE Institute of Electrical and Electronics Engineers

1

Chapter 1

Introduction

1.1 Background

Todays electric power systems are large and complex. These systems consist of many

kinds of interconnected components to generate, transmit and distribute electrical energy

continuously to a large consumers spread over the vast geographical area. Due to the

interconnection of many individual components in these systems there exist a large variety

of dynamics which can affect the system as a whole in many ways. These dynamics can

be divided into groups distinguished by their cause, consequence, time frame, physical

character or the place in the system where these dynamics occur [1]. The different Power

System dynamics are:

� Electromagnetic Transients

� Electromechanical Transients

� Quasi-Steady state Dynamics

Power system modeling and simulation is essential to satisfy operational requirements

or planning constraints [2]. In power system analysis, to deal with different dynamics,

different kinds of models are used to simulate each of the dynamic phenomena shown in

figure 1.1.

2

Chapter 1. Introduction 1.1. Background

� Electro-Magnetic Transient Model: Electro-magnetic transient phenomena oc-

curs in less than of a microsecond and involves the power systems response to

events such as lightning strikes, switching operation etc. To model these phe-

nomena, Electro-magnetic transient models are used. These models are described

mathematically by differential and algebraic equations. To use these mathematical

models in digital simulation the methods used are: state variable analysis and dif-

ference equation’s [3], [4]. A well known simulation software used to analyze these

models is EMTP-RV [5].

� Electro-mechanical Transient Model: Electro-mechanical transients occur in

the range of millisecond to seconds. An example of such transient is the oscillation of

the rotating masses of the generators and motors that occurs following a disturbance

or due to the operation a of protection system. The mathematical models of electro-

mechanical transients are simplified or averaged from electro-magnetic transient

models. This simplified mathematical models are used in digital modeling. This

simulation approach is known as phasor time domain simulation. The simulation

software packages used to analyze this kind of models are PSAT [6], EUROSTAG [7],

PSS/E [8], PSCAD [9] etc.

� Quasi-Steady State Model: Quasi-steady state (QSS) dynamics occur for more

than one second. An example of QSS is the thermodynamic change of the boiler

control action in steam power plants to meet the demand of automatic generation

controls. Mathematically, in these kind of models electro-magnetic transients are

neglected and the system is modeled by algebraic equations [10]. The only tool

used in practice for this kind of simulations is astre [11].

Figure 1.1: Time frame of different power system dynamics.

3

Chapter 1. Introduction 1.2. Problem Definition

Though there exists a lot of simulation tools, the rapid change of grid and penetration of

intermittent renewable sources making the simulation of power system challenging.

1.2 Problem Definition

Existing tools for power system phasor time domain simulation are exposed to certain

limitations such as limited simulation features [2], limited abilities for consistent model

exchange [12] or handling of penetration of new devices (FACTS).

Power system courses in the educational institutes deal with complex physical phe-

nomena and detailed mathematical models of power systems. It is difficult to visualize

the main concept of the cumbersome power system networks. Hence reproducing the

complex power system phenomena through computer-based simulations is an efficient

solution for educational and research purposes [13]. Commercially available power sys-

tem simulation software packages are used in these educational institutes. Few problems

with these software packages are: they do not allow changing the source code or adding

new parameters [14]. In order to increase the flexibility of power system simulation soft-

wares, an Open Source approach is taken by the power system academic community.

Some examples of the Open Source software packages are UWPFLOW [15], PSAT [6],

PowerWeb [16] and ObjectStab [17].

Modelica is a new promising modeling language. It is an equation based, object

oriented, open source language, offering several advantages to the modeling community. It

also offers a solution for covering model exchange challenges, easy modification of models,

easy development of custom models and providing unambiguous simulation results among

different tools [18]. One software that supports the Modelica language is OpenModelica.

At present a Power System library is developed by SmarTS Lab within the FP7 iTesla

project [19]. Most of the power system component models have already been implemented

in the library. Additional models are needed to perform time domain simulations of small

and medium sized power system networks. The problems this thesis focuses are:

� Improving the iTesla power system library with the development of new Modelica

models of power electronics based components for phasor time domain simulation.

� Validating the models and making validated test system models.

4

Chapter 1. Introduction 1.3. Objectives

� Investigating the feasibility of the models to be applied to the small and medium

power system networks such as IEEE 9-bus system and IEEE 14-bus system.

1.3 Objectives

Taking into account the problems described in the previous section, the following objec-

tives are identified for this work:

� Literature review on power system simulation methods and the contribution of

iTesla project in this field.

� How to use Modelica and PSAT for power system simulation.

� Develop the Modelica models of the Flexible AC Transmission System (FACTS)

based devices, conventional power system devices (Transformers) which are used

for hybrid electromagnetic and electromechanical power system models.

� Checking the validity of all the models against PSAT. PSAT contains the imple-

mentation of the models, which will be used in this work. So, a validation of

the simulation outputs from the Modelica models is necessary to check the same

behavior according to PSAT simulations.

� Prove the feasibility of the models into small and medium power system networks

like IEEE 9-bus and IEEE 14-bus systems.

1.4 Overview of the Report

This report is divided into three sections. In the first section, involving chapter 1 and

2, background of the project with an introduction about Modelica and PSAT is given.

In the second section, Power System component modeling in Modelica is discussed. In

this section the modeling methodology, mathematical models of the components, imple-

mentation of the models, test system for the models and software to software validation

results are given. This section covers the chapter 3 and 4. Finally in the third section,

a small discussion about the experience with Modelica and future work are summarized.

This part covers the chapter 5.

5

Chapter 2

Modeling Languages

2.1 Modelica

Modelica is an object oriented, acuasal, equation based, open source language for de-

scribing complex mathematical behavior. It supports dynamic modeling and simulation,

for complex systems and applications from different domains such as Electrical, Mechan-

ical, Hydraulic, Thermal, Control and Electric Power Engineering. Modelica models are

described in schematics (see figure 2.1).

Figure 2.1: Examples of Modelica Models [24].

6

Chapter 2. Modeling Languages 2.2. Modelica Features

Modelica Design Group develops the free library for multi-domain modeling known

as Modelica Standard Library. All the versions of the Modelica Language are available

on-line (https://modelica.org/).

2.2 Modelica Features

Modelica offers several advantages to the modeling community both in academia and

industry. Being a standard language, Modelica is supported by different modeling and

simulation tools [23]. Most important features of Modelica are [20], [21]:

� Modelica is based on equation statements instead of assignment statements. That

is why, it permits acausal modeling.

� Different domains such as Electrical, Mechanical, Thermodynamic, Hydraulic, Bi-

ological and Control applications can be connected and used in the same model.

� It provides hierarchical system architecture capabilities and visual component pro-

gramming.

� Allows the exchange of the models among simulation solvers, which are able to com-

pile Modelica code and provides unambiguous simulation results among different

tools.

� Modelica models are solver independent.

� Modelica is an object-oriented language with universal class concept that unifies

classes, generics-known as templates in C++ and general subtyping into a single

language construct. This helps evolution of models.

2.3 Modelica Simulation Environment

Modelica language is used for modeling complex mathematical problems. Different Mod-

elica simulation environments allow one to make these models using Graphical User In-

terface (GUI) editors, text-based editors or both. The currently available simulation

environments for Modelica are given in the following table 2.1. In this work Dymola [22]

and Open Modelica simulation environment is used.

7

Chapter 2. Modeling Languages 2.4. Modelica Programming

Table 2.1: Modelica based software environments.

Commercial Modelica SimulationEnvironment

Free Modelica SimulationEnvironment

Created By Name Created By Name

CyDesign LabsCyModelica, Vertex,

ConvergeModelon

ABJModelica.org

Dassault Systemes DymolaLinkopingUniversity

OpenModelica

ITI GmbH(Germany)

Simulation XINRIA

(France)SCICOS

LMSLMS

Imagine.Lab AMESimModelon AB OPTIMICA Studio

Wolfram Wolfram SystemModelerMapleSoft (Canada) MapleSim

2.4 Modelica Programming

Modelica programming can be done by using Graphical editor or writing the code in

Textual editor. In graphical editor a new model can be created by dragging and dropping

the models from the available models. Textual editor is used for writing the executable

code. That means the programming is done in the textual editor to create the models.

In the text editor model name is declared first, then the variables are declared. Finally,

the equations are added with initialization. Detail programming in Modelica text editor

can be found in [20], [21], [24].

The simulation editor is used to translate and simulate the models. Simulation editor

also used to visualize the results. One of the simple example of Modelica code is given in

figure 2.2.

8

Chapter 2. Modeling Languages 2.5. Power System Analysis Toolbox (PSAT)

Figure 2.2: Textual programming in Modelica.

2.5 Power System Analysis Toolbox (PSAT)

PSAT is a Matlab based toolbox for static and dynamic analysis of power system [6]. As

a software tool for power systems analysis, PSAT offers various routines:

� Continuation Power Flow

� Optimal Power Flow

� Small Signal Stability Analysis

� Time Domain Simulations

� Phasor Measurement Unit (PMU) placement

9

Chapter 2. Modeling Languages 2.5. Power System Analysis Toolbox (PSAT)

The main graphical user interface of PSAT is shown in figure 2.3. To make power

system networks in PSAT, one can use data files or single-line diagrams via the GUI

(using PSAT-simulink library). Then single line network or simulink diagram, is loaded

via the data file field in the main GUI. The diagram must be saved before loading. After

that this diagram is translated into PSAT readable data file and then any of available

routines can be simulated.

Figure 2.3: Graphical User Interface of PSAT.

PSAT contains different power system components models that have not yet been

modeled using Modelica. Thus, PSAT models are taken as the reference models, in order

to compare their performance against the equivalent Modelica models, developed in this

work.

10

Chapter 3

Power System Component Modeling

3.1 Introduction

In the context of the iTesla project a Modelica library is developed with different power

system components. Each of these components have been validated against their imple-

mentation in a most reliable proprietary software such as: Eurostag, PSS/E and PSAT.

The steps involved in the developing of the components successfully are:

� Read the documentation and understand the mathematical and conceptual back-

ground of the component.

� Identify all the equations, explaining the dynamic behavior of the component.

� Make a list of the parameters and variables used in these equations.

� Write the Modelica code in the text layer and use the Modelica Standard Library

when necessary.

� Initialize the model by identifying the initial conditions for both parameters and

variables.

� Carry out a software to software validation of the Modelica models against the

reference models.

11

Chapter 3. Power System Component Modeling 3.2. Power System Modeling

This work is intended to develop more components to add in the library, having PSAT

models as reference models. In this chapter, a detailed description of the developed models

and the implementation procedure in Modelica is given.

3.2 Power System Modeling

In order to develop a new power system model in Modelica three of the following items

are required.

� Components

� A connection mechanism

� A component framework

Each component is an instance of a Modelica class. Components are connected with

the connection mechanism known as connection diagram. One connection diagram is

shown in figure 3.1. The connection of components is done using connectors. Connectors

are used to create the communication link between the components. The component

framework in turn ensures that the communication between components function prop-

erly. For complex systems there exists a large number of connected components which

can be hierarchically decomposed [20].

Figure 3.1: Connection diagram for components.

3.2.1 Connectors and Connection

Modelica provides the notions of classes and objects like other object oriented program-

ming languages. In Modelica, every object is a class which defines the object behaviour

12

Chapter 3. Power System Component Modeling 3.2. Power System Modeling

and data. One of the special Modelica class is the connector class, which used to inter-

connect different components [25].

The PwPin (Power Pin) connector [23] class is the base connector used to connect the

power system components. PwPin connector is defined with four variables: Real voltage

and current (vr and ir) and Imaginary voltage and current (vi and ii). The connector is

shown in figure 3.2.

Figure 3.2: Schematic of electrical PwPin connector.

Components with the same type of connectors (PwPin) can be connected together.

This procedure is represented as an equation in Modelica. A connection between two

components is shown in figure 3.3.

Two types of couplings based on the variables are created after the connection (with

flow prefix or without): a. Equality coupling : This is for non-flow variables based

on Kirchhoffs first law. b. Sum-to-zero coupling : This is for flow variables based on

Kirchhoffs current law.

Figure 3.3: Connecting two components in Modelica.

3.2.2 Modeling Methodology

To model a power system component in Modelica some basic methodologies are followed:

13

Chapter 3. Power System Component Modeling 3.3. FACTS

� The developer can use the Modelica Standard Library to make a new model. The

input and output connectors should be labeled properly, so that users can easily

identify.

� The models should be organized in specific packages, e.g.: generator models in the

Machine package.

� Identify the parameters and use the attribute public or protected.

� All the parameters that can be modified by the user, should propagate to the top-

layer of the model, so that the user does not need to look at the bottom layer to

change any value. The developer should also define default values for the parame-

ters. The parameters should be well documented as well.

� While developing the components import all the constants from Modelica.Constants.

� The final model of the component should be a single block only. In some cases the

model is composed by own developed models or other components from the library.

In that case the developer must combine them in one final block with one icon.

3.3 FACTS

To facilitate Flexible AC Transmission System (FACTS) several devices are used. Such

FACTS devices are based on power electronics converters. They can be classified into

shunt or series devices or a combination of both [28]. The FACTS devices covered in

this thesis are Static Synchronous Compensator (STATCOM), Thyristor Controlled Se-

ries Compensator (TCSC), Static Synchronous Source Series Compensator (SSSC) and

Unified Power Flow Controller (UPFC). These models are averaged valued models, as in

PSAT. This is because in phasor time-domain simulation the aim is to observe the phe-

nomena of power system network with FACTS devices without describing in detail of the

underlying switching of the power electronics in these devices. Next subsection covers the

mathematical description of the models and the corresponding Modelica implementation.

14


3.3.1 Thyristor Controlled Series Compensator(TCSC)

TCSC is a kind of series regulator used to control the active and reactive power that flow

through the line. The regulation is based on the insertion of a series capacitive reactance

in the same line. A TCSC series controller is shown in figure 3.4.

Figure 3.4: Control block diagram of TCSC [27].

The two input signals of the regulator are line power(Pkm), reference power (Pref )

and the output signal is the series susceptance (b).

The differential equations of TCSC are:

x1 = ([xTCSC , α] +KrvPODs − x1)/Tr (3.1)

x2 = −KI(Pkm − Pref ) (3.2)

and

[xTCSC , α] = KP (Pkm − Pref ) + x2 (3.3)

where x1and x2 are the state variables. The series reactance xTCSC and the firing

angle α refer to the state variable x1.

The series susceptance b is the output signal of the regulator, given by

b(xTCSC) = −xTCSC

xkm

xkm(1 − xTCSC

xkm)

(3.4)

and for firing angle regulator

b(α) = π(k4x − 2k2

x + 1) cos kx(π − α)/[xC(πk4x cos(π − α) − π cos kx(π − α)

15


+2k4xα cos kx(π − α) + 2αk2

xα cos kx(π − α) − k4x sin 2α cos kx(π − α)

+k2x sin 2α cos kx(π − α) − 4k3

x cos2 α sin kx(π − α)

−4k2x cosαsinα cos kx(π − α))] (3.5)

here the term kx is defined by

kx =

√xCxL

3.3.2 TCSC in Modelica

Based on b(xTCSC) and b(α) two models are implemented in Modelica, named TCSCRe-

actance and another TCSCAlpha. The PwPin connector class is used in both the models.

The equations are written in the textual editor.

Reactance Model: First step in the implementation of this model in Modelica, is

to declare a set of parameters (see the code below):

model TCSCReactance

PowerSystems.Connectors.PwPin p

annotation (Placement(transformation(extent={{-119,-8},{-99,12}})));

PowerSystems.Connectors.PwPin n

annotation (Placement(transformation(extent={{100,-10},{120,10}})));

constant Real pi=Modelica.Constants.pi;

parameter Real SystemBase=100;

parameter Real Vbus=400000 "Bus nominal voltage , change of base";

parameter Real Sn=100 "Power rating , MVA";

parameter Real Vn=400000 "Voltage rating , KV";

parameter Real f=50 "Frequency rating , Hz";

parameter Real Cp=0.10 "Percentage of series compensation %";

parameter Real Tr=0.5 "Regulator time constant ,s";

parameter Real xTCSCmax=0.05 "Maximum Reactance";

parameter Real xTCSCmin= -0.05 "Minimum Reactance";

parameter Real Kp=5 "Proportional gain of PI controller p.u./p.u.";

parameter Real Ki=1 "Integral gain of PI controller p.u./p.u.";

parameter Real Kr=10 "Gain of the stabilizing signal p.u./p.u.";

parameter Real Vs_POD=0 "Power oscillation damper signal";

parameter Real x_L=0.1 "Line reactance p.u.";

16


parameter Real pref= 0.080101913348342 "Reference Power flow , p.u.";

parameter Real rL=0.01 "Line resistance , p.u.";

parameter Real x_TCSCO=0.01 "Initial series reactance TCSC p.u.";

parameter Real x20=0.01 "Initial valu of the state varible x2";

Real vk " Nominal bus voltage of bus k ";

Real vm " Nominal bus voltage of bus m";

Real pkm "Active power flow from bus k to m";

Real b;

Real x_TCSC;

Real x2(start=x20);

Real x0;

To change the value of the parameters with the system base, some parameters are defined

as protected. These are given below:

protected

parameter Real Vb2new=Vbus*Vbus;

parameter Real Vb2old=Vn*Vn;

parameter Real R=rL*(Vb2old*SystemBase)/(Vb2new*Sn);

parameter Real X=x_L*(Vb2old*SystemBase)/(Vb2new*Sn);

parameter Real xTCSC_max=xTCSCmax*(Vb2old*SystemBase)/(Vb2new*Sn);

parameter Real xTCSC_min=xTCSCmin*(Vb2old*SystemBase)/(Vb2new*Sn);

parameter Real y=1/X;

After declaring all the parameters needed, the next step is to declare the equations of

the model. So, the equations for the state variables and series susceptance, (equation 3.1,

3.2, 3.3 and 3.4) are declared in the equation section of the Modelica code. The limiters

of the regulator are implemented using a corresponding if statement. Initialization of the

state variables and reference power are taken directly from the power flow solution, cal-

culated in PSAT. Finally, the series compensation is declared by adding the susceptance

value within the line admittance. The equation section is added below:

initial equation

x_TCSC=x_TCSCO;

equation

vk=sqrt(p.vr^2+p.vi^2);

vm=sqrt(n.vr^2+n.vi^2);

if (x_TCSC >xTCSC_max) and (der(x_TCSC)>0) and (der(x2)>0) then

der(x_TCSC)=0;

17


der(x2)=-Ki*( pkm-pref);

b= -(xTCSC_max/X)/ (X*(1-(xTCSC_max/X)));

elseif (x_TCSC <xTCSC_min) and (der(x_TCSC)<0) and (der(x2)<0) then

der(x_TCSC)=0;


b= -(xTCSC_min/X)/ (X*(1-(xTCSC_min/X)));

else

der(x_TCSC)= (Kr*Vs_POD -Kp*(pkm-pref)+x2-x_TCSC)/Tr;


b= - (x_TCSC/X)/ (X*(1-(x_TCSC/X)));

end if;

pkm=(p.vr*p.ir + p.vi*p.ii);

x0=-(Kp*(pkm-pref)-x2);

p.ii=(y-b)*(n.vr-p.vr);

p.ir=(y-b)*(p.vi-n.vi);

n.ii=(y-b)*(p.vr-n.vr);

n.ir=(y-b)*(n.vi-p.vi);

Alpha Model: As this model is implemented in the same way as the reactance model,

the code is not included here.

3.3.3 Static Synchronous Compensator(STATCOM)

STATCOM is a kind of shunt connected FACTS device used to regulate reactive power

by using a Voltage Source Converter (VSC). Here the STATCOM model is a simplified

current injection model shown in figure 3.5 [27].

The differential equation of the STATCOM is:

iSH = (Kr(vref + vPODs − v) − iSH)/Tr (3.6)

The reactive power injection:

q = iSHv (3.7)

18


1r

r

K

T s

maxi

mini

v

refv

POD

sv

SHiSHi

Figure 3.5: Control block diagram of STATCOM [27].

This model has three input signals: bus voltage (v), reference voltage (vref ) and the

power oscillation damper signal (vPODs ). The output signal is the shunt current (iSH)

which is injected to the connected bus.

3.3.4 STATCOM in Modelica

Based on the control diagram of the STATCOM two models are created in Modelica. To

show different ways of modeling with Modelica, one of the models is developed using the

graphical editor (based on block diagram) and the other is developed using the textual

editor (based on equations). The graphical editor model is shown in figure 3.6.

Figure 3.6: STATCOM GUI based model in Modelica.

In the text based model the state variable and reactive power injection are calculated

using the equation 3.6 and 3.7. Then reactive power injection is related to the PwPin

variables. The limiters of the regulator are implemented using the if statement. The

Modelica code is given below:

19


model STATCOM "Static Synchronous Compensator model with equation"

PowerSystems.Connectors.PwPin p(vr(start=vr0), vi(start=vi0))

constant Real pi=Modelica.Constants.pi;


parameter Real Vbus=400000 "Bus nominal voltage , V";

parameter Real Sn=100 "Power rating , MVA";

parameter Real Vn=400000 "Voltage rating , V";

parameter Real fn=50 "Frequency rating , Hz";

parameter Real Kr=50 "Regulator gain , p.u./p.u.";

parameter Real Tr=0.01 "Regulator time constant , s";

parameter Real i_Max= 0.7 "Maximum current , p.u.";

parameter Real i_Min= -0.1 "Minimum current , p.u.";

parameter Real v_ref=1.002791151905167

"Reference voltage of the STATCOM regulator , from power flow";

parameter Real v_POD=0 "Power oscillation damper signal";

parameter Real v0=1 "Initial value of the bus voltage connected to STATCOM";

parameter Real anglev0=-0.000213067852480

"Initial angle of the Bus connected to STATCOM , from power flow";

Real i_SH;

Real v(start=v0);

Real Q;

protected

parameter Real Iold=Sn/Vn;

parameter Real Inew=SystemBase/Vbus;

parameter Real i_max=i_Max*Iold/Inew;

parameter Real i_min=i_Min*Iold/Inew;

parameter Real vr0=v0*cos(anglev0) "Initialitation";

parameter Real vi0=v0*sin(anglev0) "Initialitation";

parameter Real io= Kr*(v_ref+v_POD -v0) "Initialization";

initial equation

i_SH=io;

equation

v=sqrt(p.vr^2+p.vi^2);

0=p.vr*p.ir + p.vi*p.ii;

-Q=p.vi*p.ir - p.vr*p.ii;

if (i_SH >i_max) and (der(i_SH)>0) then

20


der(i_SH)=0;

Q=i_max*v;

elseif (i_SH <i_min) and (der(i_SH)<0) then

der(i_SH)=0;

Q=i_min*v;

else

der(i_SH)= (Kr*(v_ref+v_POD-v)-i_SH)/Tr;

Q=i_SH*v;

end if;

end STATCOM;

3.3.5 Static Synchronous Source Series Compensator(SSSC)

The SSSC is a kind of the series connected FACTS device, which is represented by a

series voltage source (see figure 3.7).

k kv

Sv

kmi

kv

kmjx

mki

m mv

Figure 3.7: Circuit diagram of SSSC [27].

The controllable parameter of SSSC is the magnitude of vS, which is kept always in

quadrature relation with the line current. The dynamic control block is shown in figure

3.8.

The input signals are line power(Pkm) and reference power (Pref ), and the output

signal is the series voltage (vS) which is injected in the line. The dynamic behavior of

21


Figure 3.8: Control block diagram of SSSC [27].

the SSSC is described by the following differential equation (calculated from the output

of the control block).

vS = (vos + vPODs − vs)/Tr (3.8)

The SSSC control depends on the input signal vos . Two different control modes are

implemented in Modelica: 1) constant voltage 2) constant power flow.

Constant Voltage: In this control mode, the input vos is constant and it does not

depend on the line current.

Constant Power Flow: In this control mode, the input signal vos is the output of

PI controller as shown in figure 3.8. The equations describing the output for this control

are :

vos = Kp(pref − pkm) + vpi (3.9)

and

vpi = KI(pref − pkm) (3.10)

3.3.6 SSSC in Modelica

The SSSC model created in Modelica has been developed considering two different control

modes: 1) Constant voltage and 2) Constant power flow. For both control modes, the

code implementation of the SSSC model is same. So only constant power flow model

implementation is discussed here.

In the Modelica model the parameters are declared first. In the equation section, the

equations for the input signals: equations 3.9 and 3.10 are written directly. Using these

two inputs, the output of the control block from equation 3.8 is calculated. This output

is the voltage, which is injected into the line. This voltage is in quadrature with the

22


current in the line, so the current angle is calculated. Then, this angle is imposed with

the voltage. In the end the injected voltage is related to the PwPin connectors. The code

of the SSSC for constant power flow mode is given below without the declaration of the

parameters:

model SSSC_CPF



initial equation

vpi=vpi0;

equation

when sample(0,0.005) then

ip=pre(p.ir);

iq=pre(p.ii);

end when;

itheta=atan2(ip ,iq);



pkm=(p.vr*p.ir + p.vi*p.ii);

if (vs >vs_max) and (der(vs)>0) then

der(vs)=0;

der(vpi)=(p_ref-pkm)*Ki;

vs0=(p_ref-pkm)*Kp+vpi;

vp= abs(vs_max)*sin(itheta);

vq= abs(vs_max)*cos(itheta);

elseif (vs<vs_min) and (der(vs)<0) then

der(vs)=0;



vp= abs(vs_min)*sin(itheta);

vq= abs(vs_min)*cos(itheta);

else

der(vs)=(vs0+vs_POD -vs)/Tr;



23


vp= abs(vs)*sin(itheta);

vq= abs(vs)*cos(itheta);

end if;

if vs >=0 then

vq=p.vr-n.vr;

vp=n.vi-p.vi;

else

vq=n.vr-p.vr;

vp=p.vi-n.vi;

end if;

p.ir=-n.ir;

p.ii=-n.ii;

annotation

end SSSC_CPF;

3.3.7 Unified Power Flow Controller(UPFC)

The UPFC is a shunt and series connected device which is modeled as a combination of

STATCOM and SSSC shown in figure 3.9. Here vS is the series voltage source and iSH

is the shunt current source.

k kv

Sv

kmi

kv

kmjx

mki

m mv

SHi

Figure 3.9: Circuit diagram of UPFC [27].

24


The equation of the series and shunt sources are

vS = (vp + vq)ejφ (3.11)

and

iSH = (ip + iq)ejθk (3.12)

The differential equations of the dynamic UPFC model are

vp = (vp0 + u1vPODs − vp)/Tr (3.13)

vq = (vq0 + u2vPODs − vq)/Tr (3.14)

iq = [Kr(vref + u3vPODs − vk) − iq]/Tr (3.15)

If the power oscillation damping signal is given then u1, u2 and u3 are 1 otherwise 0.

The dynamic model is described by the control blocks shown in figure 3.10.

Figure 3.10: Control block diagram of UPFC [27].

3.3.8 UPFC in Modelica

To implement the UPFC model in Modelica, the series and shunt components are made

in two different models. Then two models are combined together to form the complete

UPFC model. The implementation methodology of the series component is same as the

25

Chapter 3. Power System Component Modeling 3.4. Transformer

SSSC implementation and the shunt part is same as the STATCOM implementation,

with minor differences, the codes are not added here.

3.4 Transformer

Two regulating transformers (ULTC and PST) and one static transformer (TWT) are

implemented in Modelica. The detail mathematical description is given in following

sections.

3.4.1 Three-Winding Transformer(TWT)

The Three-winding Transformer is basically described as three two winding transformers

connected in star (see figure 3.11 [2]).

1nv

2nv

3nv

12z

13z

23z

1

2

3

1 1 1, /n n

z v v

0: 1a

2 1 2, /n n

z v v

3 1 3, /n n

z v v

Figure 3.11: Equivalent circuit: Three-Winding Transformer [27].

The star impedances of the triangle branches are:

z12 = z1 + z2

z13 = z1 + z3

z23 = z2 + z3

(3.16)

26


Thus

z1 = (z12 + z13 − z23)/2

z2 = (z12 + z23 − z13)/2

z3 = (z13 + z23 − z12)/2

(3.17)

3.4.2 TWT in Modelica

The two winding transformer in Modelica is modeled as a transmission line with only

series impedance without iron losses [23]. Three Winding Transformer is implemented by

using the method of equivalent three two-winding transformers (see the three branches of

transformer in figure 3.11), but in the case of Three Winding Transformer the impedances

are taken as a resulting star impedance (equation 3.17); in the first branch a fixed tap

ratio is taken into account. The code for first branch is given in following:

model Branch1 "First winding of Three Winding Transformer"


PowerSystems.Connectors.PwPin n1


parameter Real Sn=100 "Power rating MVA";

parameter Real Vbus=400000 "Sending end bus voltage , V";

parameter Real Vn1=400000 "Voltage rating of the first winding , V";

parameter Real Vn2=100000 "Voltage rating of the second winding , V";

parameter Real Vn3=40000 "Voltage rating of the third winding , V";

parameter Real fn=50 "Frequency rating , Hz";

parameter Real R12=0.01 "Resistance of the branch 1-2, p.u.";



parameter Real X12= 0.1 "Reactance of the branch 1-2, p.u.";



parameter Real m=0.98 "Fixed Tap ratio";

Real r1;

Real x1;

Real anglev2 "Angle of the fictious bus";

Real vbus2 "Voltage of the fictious bus";

27


equation

vbus2=sqrt(n1.vr ^2+n1.vi ^2);

anglev2=atan2(n1.vi , n1.vr);

r1=0.5*(R12+R13-R23);

x1=0.5*(X12+X13-X23);

r1*p.ir-x1*p.ii= (1/m^2)*p.vr- (1/m)*n1.vr;

r1*p.ii+x1*p.ir= (1/m^2)*p.vi- (1/m)*n1.vi;

r1*n1.ir-x1*n1.ii= n1.vr- (1/m)*p.vr;

x1*n1.ir+r1*n1.ii= n1.vi- (1/m)*p.vi;

end Branch1;

After making three branches in the same way, all three branches are connected (see figure

3.12). Finally, all the parameter of these three branches are declared in upper label (by

using the component reference) to finalize the model.

Figure 3.12: Three Winding Tansformer in Modelica.

3.4.3 Under Load Tap Changer

The Under Load Tap Changer is a kind of regulating transformer. The equivalent pi

circuit and the secondary voltage control scheme control of ULTC is shown in figure 3.13

and 3.14. If the tap ratio step ∆m = 0 then:

m = m (3.18)

To control the voltage and reactive power:

m = −Hm+K(vm − vref )

m = −Hm+K(qref + qm)(3.19)

28


where, H is the integral deviation, K is the inverse time constant, vm is secondary bus

voltage and vref is the reference voltage.

Figure 3.13: Equivalent π circuit: Under Load Tap Changer [27].

K

H s

maxm

minm

refv m

dead zone

LTC &

Networkmvm

Figure 3.14: Secondary voltage control scheme of ULTC [27].

3.4.4 ULTC in Modelica

In Modelica, the implementation of the ULTC is a continuous model so the tap ratio step

taken is ∆m = 0. The model is implemented using the PwPin connector for inputs and

outputs. To calculate the current variable of the connector, equation 3.20 is used (using

equivalent π circuit [2]). To calculate the dynamic tap ratio m, the equation 3.19 is used.

The limits of the controller are implemented using the if statement. The Modelica code

is given below: [ik

im

]= y

[1m2 − 1

m

− 1m

1

][vk

vm

](3.20)

model ULTC_VoltageControl

"Under Load Tap Changer , continous model , secondary voltage control"

29





parameter Real Vbus1=400000 "Sending end Bus nominal voltage , change of base";

parameter Real Vbus2=100000 "Receiving end Bus voltage , change of base";

parameter Real Sn=100 "Power rating MVA";

parameter Real Vn=400000 "Voltage rating , primary side KV";

parameter Real fn=50 "Frequency rating Hz";

parameter Real kT=4 "Nominal Tap ratio (V1/V2), kV/kV";

parameter Real H=0.001 "Integral deviation , p.u.";

parameter Real K= 0.10 "Inverse time constant , 1/s";

parameter Real m_max=0.98 "Max tap ratio , p.u./p.u.";

parameter Real m_min=0.9785 "Min tap ratio , p.u./p.u.";

parameter Real deltam=0 "Tap ratio step , p.u./p.u.";

parameter Real v_ref=1.0 "Reference voltage , p.u.";

parameter Real xT= 0.001 "Transformer Reactance , p.u.";

parameter Real rT=0.1 "Transformer Resistance , p.u.";

parameter Real d= 0.05 "Dead zone percentage , %";

parameter Real vm0=1.008959700699460

"Initial value of the voltage of the Controlled Bus";

parameter Real m0=0.98;

Real m "Tap ratio";

Real vk "Voltage at primary , p.u.";

Real vm "Voltage at secondary p.u.";

Real anglevk "Angle at primary";

Real anglevm "Angle at secondary ";

protected

parameter Real V2= Vn/kT "Secondary voltage";

parameter Real Vb2new=Vbus1*Vbus1;

parameter Real Vb2old=Vn*Vn;

parameter Real R=rT*(Vb2old*SystemBase)/(Vb2new*Sn)

"Transformer Resistance , p.u.";

parameter Real X=xT*(Vb2old*SystemBase)/(Vb2new*Sn)

"Transformer Reactance , p.u.";

parameter Real vref=v_ref*(V2/Vbus2);

initial equation

m=m0;

equation

30




anglevk=atan2(p.vi , p.vr);

anglevm=atan2(n.vi , n.vr);

if (m>m_max) and (der(m)>0) then

R*p.ir-X*p.ii= (1/ m_max^2)*p.vr- (1/m_max)*n.vr;

R*p.ii+X*p.ir= (1/ m_max ^2)*p.vi- (1/m_max)*n.vi;

R*n.ir-X*n.ii= n.vr- (1/ m_max)*p.vr;

X*n.ir+R*n.ii= n.vi- (1/ m_max)*p.vi;

der(m)=0;

elseif (m<m_min) and (der(m)<0) then

R*p.ir-X*p.ii= (1/ m_min^2)*p.vr- (1/m_min)*n.vr;

R*p.ii+X*p.ir= (1/ m_min ^2)*p.vi- (1/m_min)*n.vi;

R*n.ir-X*n.ii= n.vr- (1/ m_min)*p.vr;

X*n.ir+R*n.ii= n.vi- (1/ m_min)*p.vi;

der(m)=0;

else

R*p.ir-X*p.ii= (1/m^2)*p.vr- (1/m)*n.vr;

R*p.ii+X*p.ir= (1/m^2)*p.vi- (1/m)*n.vi;

R*n.ir-X*n.ii= n.vr- (1/m)*p.vr;

X*n.ir+R*n.ii= n.vi- (1/m)*p.vi;

der(m)= -(H*m)+K*(vm-vref);

end if;

end ULTC_VoltageControl;

3.4.5 Phase Shifting Transformer(PST)

Equivalent circuit and control block of phase shifting transformer are shown in figure 3.15

and 3.16.

The differential equations describing the PST transformer are given by:

α = Kp(pk − pmes)/Tm +Ki(pmes − pref )

pmes = (pk − pmes)/Tm(3.21)

31


y m

21 mym

1m ym

kv

1 :1je mv mv

Figure 3.15: Equivalent circuit of Phase Shifting Transformer [27].

p iK s K

s

minmesp

max

refpPHS &

Network

1

1mT s

kp

Figure 3.16: Control scheme of Phase Shifting Transformer [27].

where, α is the phase angle, pmes is the measured power flow, pk is the real power

flow. Ki, Kp, Tm are integral gain, proportional gain and measurement time constant,

respectively.

3.4.6 PST in Modelica

In Modelica the implementation of the PST model is similar to the ULTC model but, in

this case, the tap ratio is fixed and the angle is changed. The final model is implemented

by using two sub models. First, the fixed tap ratio and line impedance (see figure 3.15)

are declared, using the following code structure:

equation



32




R*p.ir-X*p.ii= (1/m^2)*p.vr- (1/m)*n.vr;

R*p.ii+X*p.ir= (1/m^2)*p.vi- (1/m)*n.vi;

R*n.ir-X*n.ii= n.vr- (1/m)*p.vr;

X*n.ir+R*n.ii= n.vi- (1/m)*p.vi;

Next the controller (figure 3.16) equations (equation 3.21) are declared in another part.

The relation between PST angle alpha with PwPin connector variables are calculated by

using the relation v′m : vm = 1ejα : 1 (see figure 3.15). Finally, both parts are added

together to make the final model. The implementation of the controller part is given

below (only the equation section):

initial equation

alpha=alpha0;

pmes=pmes0;

equation





if (alpha >alpha_max) and (der(alpha)>0) and (der(pmes)>0) then

der(alpha)=0;

der(pmes)=(pk-pmes)/Tm;

p.vr=n.vr*cos(alpha_max)-n.vi*sin(alpha_max);

p.vi=n.vr*sin(alpha_max)+n.vi*cos(alpha_max);

p.ir+n.ir=0;

p.ii+n.ii=0;

elseif (alpha <alpha_min) and (der(alpha)<0) and (der(pmes)<0) then

der(alpha)=0;


p.vr=n.vr*cos(alpha_min)-n.vi*sin(alpha_min);

p.vi=n.vr*sin(alpha_min)+n.vi*cos(alpha_min);

p.ir+n.ir=0;

p.ii+n.ii=0;

else

33


der(alpha)= (Kp*(pk-pmes)/Tm)+Ki*(pmes-pref);


p.vr=n.vr*cos(alpha)-n.vi*sin(alpha);

p.vi=n.vr*sin(alpha)+n.vi*cos(alpha);

p.ir+n.ir=0;

p.ii+n.ii=0;

end if;

end pst2;

34

Chapter 4

Power System Model Validation

At this stage, Modelica models have to be validated against their reference model. A

software to software validation has to be performed. For this task, simple test scenario is

modeled in both Modelica and PSAT. In both scenarios, the same perturbation is applied.

This will allow the comparison of the simulation results generated by both modeling tools.

More details on the test models are described in the following sections.

4.1 Simulation Setup

The simulation set up used for the validation is given in table 4.1.

Table 4.1: Simulation set up for the validation.

Set up Modelica PSAT

Simulation Environment Dymola Matlab

Integration Algorithm Dassl [22] Trapezoidal Rule

Time step .01s .01s

Tolerance .00001 .00001

Power flow Not implemented yet Newton Raphson method

35

Chapter 4. Power System Model Validation 4.2. Initialization

4.2 Initialization

Prior to a power system time domain simulation, the power flow calculation needs to be

done for computing the steady-state values of the network, which are used to initialize

the models for dynamic simulations. Due to multi-domain behavior of Modelica, it lacks

a power flow computation method. So the power flow calculation is done with another

power system analysis software, in this case PSAT, and the values are used to initialize

the corresponding Modelica model. The initialization done in two ways [26]:

� Start values for variables.

� Initial equations and initial algorithms.

One of the problems when modeling with mathematical equations is to determine how

many initial conditions are required to have a well-posed model. The answer is that

there should be the same number of initial equations as states of the system [21]. In any

model, the variables being differentiated are known as the state variables. To initialize

these variables, the derivative of the state variables is taken as zero to form the equation.

Then, the initial equations can be solved with the help of power flow calculations. All

the initial equations used are given below, and in the case of the TCSC, the initialization

is carried out by setting the start values directly from power flow solution.

� STATCOM:

iSH0 = Kr(vref + vPODs − v0)

� SSSC:

vs0 = vos + vPODs

� UPFC:

iq0 = Kr(vref + u3vPODs − vk0)

vp0 = vp0 + u1vPODs

vq0 = vq0 + u2vPODs

36

Chapter 4. Power System Model Validation 4.3. Validation of FACTS Devices

4.3 Validation of FACTS Devices

All the FACTS devices developed in this work are, in simple terms: regulators. Every

regulator output undergoes a limiter. In order to check the upper and lower limit of

these limiters a hit limit test has been implemented. In the same hit limit test, the loads

are also changed for a certain time. The validation scenarios with the perturbation are

discussed in the following sections.

4.3.1 Validation of TCSC model

For the two TCSC models, the same model has been created in both Modelica and PSAT,

for validating the outputs. The test model consists of a simple network with three buses,

one synchronous generator (Second Order) in the bus [1] and a TCSC placed between

bus [1] and bus [2] to control the power flow. In bus [3], a PQ load is placed. In Modelica

as transmission line parameters are included in the TCSC, there is no need to put an

additional transmission line. The test models are shown in the figures 4.1 and 4.2. To

compare the dynamic response of both models, the same perturbation is applied:

Synchronous Machine:

� Vf , square oscillation −0.045 ∗ square(2π ∗ 0.1 ∗ t) from time 0s to 20s.

PQ Load

� P , an active load is added to hit the limit of the limiter of the regulator +.01 from

time 2s to 10s and −.01 from time 12s to 20s.

� Q, a reactive load is added to hit the limit of the limiter of the regulator +.01 from

time 2s to 10s and −.01 from time 12s to 20s.

4.3.2 Simulation Result of TCSC validation

Simulation outputs from Modelica and PSAT simulations are shown in figure 4.3 and

4.4. The validation procedure compares the output signals by changing the generator

37


(a) In PSAT.

(b) In Modelica.

Figure 4.1: Test Model of TCSC type: Reactance.

(a) In PSAT.

(b) In Modelica.

Figure 4.2: Test Model of TCSC type: Alpha.

field voltage [vf ] and P, Q values of the loads. The TCSC is used to control the power

flow [Pij] between Bus [1] and Bus [2] by controlling the line susceptance [b]. Due to

changes in load, the TCSC susceptance changes accordingly keeping the power flow same

as reference power [Pref ]. Due to limit[ xmaxTCSC , xminTCSC and αmax, αmin ] provided to the

state variables [x1 and x2], the susceptance and states variables reach the upper and

lower limit (see in figure 4.3 and 4.4 the state variable x1 in the upper right plot).

38


0 5 10 15 20 250.96

0.98

1

1.02

1.04

1.06

1.08

Time(s)

V(f

)

DymolaPSAT

0 5 10 15 20 25−0.05

0

0.05

Time(s)

x1

DymolaPSAT

0 5 10 15 20 25−0.08

−0.06

−0.04

−0.02

0

0.02

Time(s)

x2

DymolaPSAT

0 5 10 15 20 25−0.15

−0.1

−0.05

0

0.05

0.1

Time(s)

x0T

csc

DymolaPSAT

Figure 4.3: Software to software validation of TCSC Reactance Model.

0 5 10 15 20 250.96

0.98

1

1.02

1.04

1.06

1.08

Time(s)

V(f

)

DymolaPSAT

0 5 10 15 20 250.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

Time(s)

x1

DymolaPSAT

0 5 10 15 20 250.74

0.76

0.78

0.8

0.82

0.84

Time(s)

x2

DymolaPSAT

0 5 10 15 20 250.65

0.7

0.75

0.8

0.85

0.9

Time(s)

x0T

csc

DymolaPSAT

Figure 4.4: Software to software validation of TCSC Alpha Model.

39


These results state that the simulation of the TCSC model yields the same result in both

software tools.

4.3.3 Validation of STATCOM model

To validate the two STATCOM models described in this work, two test models are created

in Modelica and one in PSAT (see figure 4.5). These simple test systems are composed

of three buses, with the STATCOM model connected at bus [2], to control the voltage

at bus [2]. Two perturbations are applied in the test system, affecting the generator and

load:

Synchronous Machine:

� Vf , square oscillation −0.045 ∗ square(2π ∗ 0.1 ∗ t) from 0s.

PQ Load

� Q, reactive load is added to hit the limit of the limiter of the regulator +.42 from

8s

40


(a) In PSAT.

(b) In Modelica [Text Based Model].

(c) In Modelica [GUI Based Model].

Figure 4.5: Test Model of STATCOM.

4.3.4 Simulation Result of STATCOM

Simulation outputs are shown in figure 4.6 and A.4. The perturbation applied in the

generator field voltage [vf ] and in the reactive load [Q] in Bus [2], affects the voltage of

Bus [2]. STATCOM keeps the Bus [2] voltage within the limit by injecting current [iSH ]

(see figure 4.6 and A.4). The current injection also reaches its limit [imax, imin] in oder

to keep the bus voltage stable. The results of both the softwares are similar.

41


0 5 10 15 20 25−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

Time(s)

δ (G

en 1

)

DymolaPSAT

0 5 10 15 20 250.9999

0.9999

0.9999

1

1

1

1

1

Time(s)

ω (

Gen

1)

DymolaPSAT

0 5 10 15 20 250.95

1

1.05

Time(s)

V[B

us 2

]

DymolaPSAT

0 5 10 15 20 25−0.2

0

0.2

0.4

0.6

0.8

Time(s)

i SH

DymolaPSAT

Figure 4.6: Software to software validation of STATCOM GUI based Model.

4.3.5 Validation of SSSC model

To validate SSSC model for both of the modes, a test system is created composed of

three buses. The SSSC is placed between Bus [1] and Bus [2]. The perturbation applied

to the test system is as described in the validation of the TCSC model. The test models

are shown in figure 4.7 and 4.8. The simulation the result of constant power flow SSSC

model is shown in figure 4.9 and result of constant voltage model is added in figure A.5.

Figure 4.7: Test Model of SSSC in PSAT.

42


Figure 4.8: Test Model of SSSC in Modelica.

Figure 4.9: Software to software validation of SSSC in constant power mode.

4.3.6 Validation of UPFC model

To validate the UPFC model, a three bus test system is created and the UPFC is placed

between bus [2] and [3]. The perturbation applied is same as the TCSC but, in this case,

the PQ loads are varied by .02 p.u. The test systems are shown in figure 4.10. The

simulation result of UPFC are shown in figure 4.11.

43


(a) In PSAT.

(b) In Modelica.

Figure 4.10: Test Model of UPFC.

Figure 4.11: Software to software validation of UPFC in constant power mode.

44

Chapter 4. Power System Model Validation 4.4. Transformer

4.4 Transformer

Three different test systems have been implemented for the validation of the TWT,

ULTC and PST transformer models (see figures 4.12, 4.13 and 4.14). Also, different

perturbations have been applied in the test systems models:

Synchronous Machine for all cases:

� Vf , sinusoidal oscillation −0.001 ∗ sin(2π ∗ 0.2 ∗ t) from time 0s to 5s.

PQ Load for TWT and ULTC

� Q, a reactive load is added +.01 (for ULTC +.05) from time 5s to 8s and −.01 (for

ULTC −.05) from time 8s to 12s.

PQ Load for PST

� P , an active load is added +.02 from time 5s to 8s and −.02 from time 8s to 12s.

� Q, a reactive load is added +.01 from time 5s to 8s and −.01 from time 8s to 12s.

(a) In PSAT.

(b) In Modelica.

Figure 4.12: Test Model of TWT.

45

Chapter 4. Power System Model Validation 4.5. Transformer Simulation Result

(a) In PSAT.

(b) In Modelica.

Figure 4.13: Test Model of ULTC.

(a) In PSAT.

(b) In Modelica.

Figure 4.14: Test Model of PST.

4.5 Transformer Simulation Result

Modelica simulation outputs are, again, compared against the reference model developed

in PSAT. The following results show the comparison between Modelica and PSAT sim-

ulations for the ULTC model (The simulation results of TWT and PST simulations are

included in the figure A.6 and A.7). The dynamic tap ratio m of ULTC is used to control

the Bus[3] voltage. Due to the changes of load at Bus [3] (see the perturbation applied)

the tap ration m varies (see figure 4.15). The variation of tap ratio is consistent in both

the software packages.

46

Chapter 4. Power System Model Validation 4.6. IEEE Standard Test System

0 5 10 15 20−0.03

−0.02

−0.01

0

0.01

Time(s)

δ

DymolaPSAT

0 5 10 15 201

1

1

1

1

1

1

Time(s)

ω

DymolaPSAT

0 5 10 15 201

1.005

1.01

1.015

1.02

1.025

Time(s)

Vbu

s [3

]

DymolaPSAT

0 5 10 15 200.9785

0.979

0.9795

0.98

0.9805

0.981

Time(s)

m

DymolaPSAT

Figure 4.15: Software to software validation of ULTC.

4.6 IEEE Standard Test System

Having the Modelica implementation and validation of all the components described

above, IEEE 9-Bus and 14-Bus test system is implemented and tested with the compo-

nents developed in this work.

4.6.1 IEEE 9-Bus Test System

The IEEE 9-Bus Test System represents a portion of the Western System Coordinating

Council (WSCC) [29] (The single line diagram of the IEEE 9-Bus system with the com-

plete data is given in Appendix A.3.1). Four different versions of the 9-Bus test system

were implemented in Modelica: (a) STATCOM is connected in bus 8 and the (b) TCSC,

(c) SSSC and (d) UPFC are connected in between bus 8 and bus 9. The system with

STATCOM is shown in figure 4.16 and the system with TCSC is shown in figure A.1.

47


(a) In PSAT.

(b) In Modelica.

Figure 4.16: IEEE 9-Bus Test system.

4.6.2 IEEE 14-Bus Test System

The IEEE 14-Bus Test case represents a portion of the American Electric Power System

which is located in the Midwestern US [30].(The single line diagram of the IEEE-14 Bus

system with the complete data is given in Appendix A.3.2). An available model of this

system is already implemented in PSAT. For the Modelica implementation of this system,

the Power System Library and developed components in this work have been used. A

scenario with the presence of small disturbances is modeled in both simulation tools, to

observe and compare its dynamic behavior. The ULTC and PST were placed in between

48


Bus 4 and Bus 9 (see figures 4.17 and 4.18) in two different IEEE 14-Bus test systems.

In the case of the TWT, the TWT is placed between Bus 4, Bus 8 and Bus 9 in another

IEEE 14-Bus system (shown in figure A.2 and A.3). In this case Bus 7 is not used as it

becomes a fictitious bus inside the TWT. All these test systems were also implemented

in PSAT.

Figure 4.17: IEEE 14-Bus Test system in PSAT with ULTC.

49


Figure 4.18: IEEE 14-Bus Test system in Modelica with ULTC.

4.6.3 Quantitative Assessment

The qualitative observation only provide an insight of the validity of a model. In contrast,

a quantitative assessment allows to measure the validity of a model response against its

reference in numerical metrics. For the validation of small test systems only qualitative

assessment is done, but for IEEE 9-Bus and 14-Bus systems, results of two different

software packages are analyzed both graphically and numerically. The quantitative as-

sessment is carried out using the Root Mean Square Error (RMSE) [31]. The RMS value

of the error is calculated using the equation:

ZRMSE =√

1/n[(x1 − y1)2 + (x2 − y2)2 + ...+ (xn − yn)2] (4.1)

where, x1, x2, ..., xn are the discrete measurement point at time t1, t2, ..., tn for software

package (a) and y1, y2, ..., yn are the discrete measurement points at time t1, t2, ..., tn for

software package (b). ZRMSE is the RMS value of the error of Z variable.

50


4.6.4 Simulation Result of IEEE 9 and 14-Bus Test System

The time domain simulations were executed in OpenModelica (OM) for IEEE 9-Bus

test system and in Dymola for IEEE 14-Bus test system. The system is initialized with

the power flow solution calculated in PSAT. In the test cases of IEEE 9-bus the same

perturbation is applied: three phase fault is applied in bus 8 at 3s with clearing time

100ms. For IEEE 14-bus test system scenarios simulates a fault at bus 9, which occurs

at 10s from the start of the simulation, with a clearing time of 100ms. The simulation of

is done for 25s.

The solver used in both the softwares is Rungekutta. 1 The simulations were done for

25s, with a time step of 0.001s. The RMSE was calculated using 25000 points from both

simulation results and for different state variables and for all the tests using equation 4.1.

This calculation was performed using Matlab. The RMS error values are given in Table

4.2.

Table 4.2: Calculations using equation 4.1

.

Model and Variable RMSE Model and Variable RMSE

STATCOM (iSH) 2.8011 ∗ 10−6 UPFC (vq) 3.5200 ∗ 10−6

TCSC (x1) 2.7316 ∗ 10−6 ULTC (m) 3.5439 ∗ 10−6

TCSC (x2) 2.6072 ∗ 10−6 PST (α) 6.7955 ∗ 10−4

SSSC (vs) 6.9862 ∗ 10−6 PST (Pmes) 6.795 ∗ 10−4

SSSC (vpi) 4.5086 ∗ 10−6 TWT (VINTBus) 7.5164 ∗ 10−4

UPFC (iq) 4.6006 ∗ 10−5

Illustration of the software to software validation result of IEEE 9-Bus with STAT-

COM is given in figure 4.19 and results with TCSC, SSSC and UPFC are given in figures

A.8, A.9 and A.10. The simulation result of IEEE 14-Bus test system with ULTC is given

in figure 4.20 and results with PST and TWT is given in figures A.11 and A.12.

1Runge-Kutta, second order, fixed time step method.

51


0 5 10 15 20 250.9994

0.9995

0.9996

0.9997

0.9998

0.9999

1

1.0001

1.0002

Time(s)

ω

OM [ω1]PSAT [ω1]OM [ω2]PSAT [ω2]OM [ω3]PSAT [ω3]

0 5 10 15 20 250.115

0.12

0.125

0.13

0.135

0.14

0.145

0.15

Time(s)

iSH

OMPSAT

Figure 4.19: Software to software validation results of IEEE 9-Bus with STATCOM.

0 5 10 15 20 250.965

0.966

0.967

0.968

Time(s)

Con

tinuo

us T

ap

DymolaPSAT

0 5 10 15 20 250.998

0.999

1

1.001

Time(s)

ω [G

en1]

DymolaPSAT

0 5 10 15 20 250.9

0.95

1

1.05

1.1

Time(s)

Vbu

s [9

]

DymolaPSAT

0 5 10 15 20 251

1.05

1.1

1.15

Time(s)

Vbu

s [8

]

DymolaPSAT

0 5 10 15 20 253

3.5

4

4.5

Time(s)

P [G

en1]

DymolaPSAT

0 5 10 15 20 25−0.6

−0.4

−0.2

0

0.2

Time(s)

Q [G

en1]

DymolaPSAT

Figure 4.20: Software to software validation results of IEEE 14-Bus with ULTC.

52

Chapter 5

Discussion and Conclusion

5.1 Modelica

In this thesis, Modelica based power system component modeling, simulation and software

to software validation is presented. Modelica is an object-oriented, structured mathemat-

ical language, has the ability to exchange the models to different numerical solvers. It is

advantageous in a sense that the users do not need to write code to explicitly transport

data between objects through assignment statements or message passing code like other

object-oriented languages. The code is automatically generated by the Modelica com-

piler based on the declared equations. Moreover acausal modeling allows reusability of

the models as in acausal modeling it is not required to specify a certain data flow direc-

tion. In addition Modelica offers different powerful mathematical solvers in the Modelica

simulation environment which gives the users much more choice to have the best results.

As an example figure 5.1 shows the comparison of three different solvers available in

Open Modelica: Runge-Kutta, Dassl (Differential Algebraic System Solver) and Euler

with Trapezoidal solver available in PSAT (with TCSC in IEEE 9-Bus). Basically due to

efficient simulation and ease of use made Modelica a better choice to the modeling and

simulation community. Another advantage of using Modelica is simulation time required

less in Modelica. figure 5.2 shows the time required to simulate the IEEE 9-Bus system

including TCSC using different solvers whereas the average simulation time took in PSAT

with six different tolerances is 608 s.

53

Chapter 5. Discussion and Conclusion 5.1. Modelica

0 5 10 15 20 25

−0.025

−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

Time(s)

x1

RungeKutta

Trapezoidal

Dassl

Euler

6.3 6.4 6.5

6.2

6.4

6.6

x 10−3

Figure 5.1: Comparison of different solvers of Open Modelica with Trapezoidal rule ofPSAT.

1e−10 1e−08 1e−06 1e−0510

0

101

102

103

Tolerance

Tim

e

EulerTrapezoidalRungeKuttaDassl

Figure 5.2: Total simulation time spending for the solvers in Open Modelica with differenttolerance.

54

Chapter 5. Discussion and Conclusion 5.2. Modeling and validation

5.2 Modeling and validation

In the chapter 3, a detailed description of the power system component modeling is given.

Prior to this work most of the components based on PSAT reference already developed.

In this work the components developed also based on PSAT reference. In Modelica one

can use the already developed components to make a new model in some cases. In case

of one model (STATCOM) existing Modelica components is used. All other models are

developed based on the equation declaration method. This proves that Modelica models

can be implemented using the existing Modelica tools and/or using previously developed

models. Modelica provides more flexibility and better understanding of the models, means

one can easily understand what is programmed by seeing the source code. Most of other

modeling methods it is difficult to understand only by accessing the source code of the

model. The validation results and the dynamic behavior matches (with small difference)

with the reference software package which proves that Modelica can be adapted as an

universal modeling language.

In chapter 4 and Appendix A all the model validation results are given. After imple-

menting the simple test system, more complex system like IEEE 9-bus and IEEE 14-bus

test systems are implemented. The simulation result of the complex systems also consis-

tent with the reference software: PSAT result, but in case of big system the simulation

time requires more. This can be improved by further simplifying of the models and also

Modelica developers are working on better simulation performance.

5.3 Conclusion

The models simulated in two different software packages accurately predict the same

dynamic behavior, so it cannot be said that one is better than other; rather the modeling

community is free to choose the modeling language. The results show that the Modelica

language is capable of providing similar results of those of typical power system simulation

tools for time-domain analysis, and thus, the added values of the Modelica language

(model portability and accessibility, and a standardized modeling language) can be fully

exploited for power system simulation.

55

Chapter 6

Future Work

6.1 Future work

This work is applicable for the time domain simulation of cyber-physical power system

components. However, the lack of a power flow computation tools make the Modelica

models depend on other software tools to compute the steady-state conditions of a power

system. An approach to initiate a power flow solver adapted by Modelica tools can be

completed.

Regarding the models developed in this work, some improvements have been identified.

In case of the ULTC, the model implemented in this work is a continuous model. The

ULTC model can be improved by combining the continuous and discontinuous operations

of this kind of transformer.

The oscillation damper input has not tested for any of the FACTS models, in future

work it can be shown how this damper signal improve the oscillatory stability. This can

be carried out using both averaged models and detailed switching models that can be

implemented through equation based modeling in future.

56

Appendix A

Test System and Validation

A.1 Test System

Figure A.1: IEEE 9-Bus Test system with TCSC Reactance Model (between Bus 8 andBus 9) in OpenModelica.

57

Chapter A. Test System and Validation A.1. Test System

Figure A.2: IEEE 14-Bus Test system with PST (Between Bus 4 and Bus 9) in Modelica.

Figure A.3: IEEE 14-Bus Test system with TWT in Modelica.

58

Chapter A. Test System and Validation A.2. Software to Software Validation

A.2 Software to Software Validation

0 5 10 15 20 25−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

Time(s)

δ (G

en 1

)

DymolaPSAT

0 5 10 15 20 250.9999

0.9999

0.9999

1

1

1

1

1

Time(s)

ω (

Gen

1)

DymolaPSAT

0 5 10 15 20 250.95

1

1.05

Time(s)

V[B

us 2

]

DymolaPSAT

0 5 10 15 20 25−0.2

0

0.2

0.4

0.6

0.8

Time(s)

i SH

DymolaPSAT

Figure A.4: Software to software validation of STATCOM Text based Model.

Figure A.5: Software to software validation of SSSC in constant voltage mode.

59


Figure A.6: Software to software validation of TWT.

Figure A.7: Software to software validation of PST.

60


0 5 10 15 20 25−0.03

−0.02

−0.01

0

0.01

0.02

Time(s)

x1

OMPSAT

0 5 10 15 20 254

6

8

10

12x 10

−3

Time(s)

x2

OMPSAT

0 5 10 15 20 251

1.005

1.01

1.015

Time(s)

V [B

us 8

]

OMPSAT

0 5 10 15 20 25−0.3

−0.2

−0.1

0

0.1

0.2

Time(s)x0

OMPSAT

Figure A.8: Software to software validation of IEEE 9-Bus system with TCSC.

0 5 10 15 20 25−0.03

−0.02

−0.01

0

0.01

0.02

Time(s)

vs

OMPSAT

0 10 20 30−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

Time(s)

vpi

OMPSAT

0 10 20 30−1

−0.5

0

0.5

1

Time(s)

vs0

OMPSAT

Figure A.9: Software to software validation of IEEE 9-Bus system with SSSC.

61


0 5 10 15 20 250

0.05

0.1

0.15

0.2

Time(s)

iq

OMPSAT

0 10 20 307.956

7.957

7.958

7.959

7.96

7.961x 10

−3

Time(s)

vq

OMPSAT

0 10 20 301

1.01

1.02

1.03

1.04

1.05

1.06

Time(s)

V [B

us 9

]

OMPSAT

Figure A.10: Software to software validation of IEEE 9-Bus system with UPFC.

62


0 5 10 15 20 250.04

0.045

0.05

0.055

0.06

0.065

Time(s)

α

DymolaPSAT

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

Time(s)

pmes

DymolaPSAT

0 5 10 15 20 250.9

0.95

1

1.05

1.1

Time(s)

Vbu

s [9

]

DymolaPSAT

0 5 10 15 20 253.2

3.4

3.6

3.8

4

4.2

Time(s)

P [G

en1]

DymolaPSAT

Figure A.11: Software to software validation of IEEE-14 Bus system with PST.

0 5 10 15 20 250.9

0.95

1

1.05

1.1

1.15

Time(s)

V [I

nter

nal F

ictit

ious

Bus

, TW

T]

DymolaPSAT

0 5 10 15 20 25−3

−2.5

−2

−1.5

−1

−0.5

0

Time(s)

Ang

le [I

nter

nal F

ictit

ious

Bus

, TW

T]

DymolaPSAT

0 5 10 15 20 250.9

0.95

1

1.05

1.1

Time(s)

Vbu

s [9

]

DymolaPSAT

0 5 10 15 20 250.998

0.9985

0.999

0.9995

1

1.0005

Time(s)

ω [G

en1]

DymolaPSAT

Figure A.12: Software to software validation of IEEE 14-Bus system with TWT.

63

Chapter A. Test System and Validation A.3. Test System Data

A.3 Test System Data

A.3.1 9 Bus Test System

The complete data of IEEE 9-Bus test system (shown in figure A.13) is given below:

Figure A.13: WSCC 9-Bus test System [27].

Table A.1: Synchronous Generator Data

Parameter Symbol Unit Generator 1 Generator 2 Generator 3

Bus Number - - 1 2 3

Power rating Sn MVA 100 100 100

Voltage rating Vn kV 16.5 18 13.8

Frequency rating fn Hz 60 60 60

Machine order - - 4 4 4

Armature resitance ra p.u. 0 0 0

d-axis synchronous reactance xd p.u. .1460 .8958 1.3125

d-axis transient reactance x′d p.u. .0608 .1198 .1813

d-axis sub-transient reactance x′′d p.u. 0 0 0

d-axis open circuit transient time constant T ′d0 s 8.96 6 5.89

q-axis synchronous reactance xq p.u. .0969 .8645 1.2578

q-axis transient reactance x′q p.u. .0969 .1969 .2500

q-axis sub-transient reactance x′′q p.u. 0 0 0

q-axis open circuit transient time constant T ′q0 s .310 .5350 0.6

Mechanical starting time M = 2H kWs/kVA 47.28 12.80 6.02

Damping Coefficent D - 0 0 0

Speed feedback gain Kw gain 0 0 0

Active power feedback gain KP gain 0 0 0

64


Table A.2: Line Data

Line From Bus To Bus Resistance (r, p.u.) Reactance (x, p.u.)Shunt

susceptance (b, p.u.)

Line 9 8 .0119 .1008 .209

Line 1 7 8 .0085 .072 .149

Line 2 9 6 .039 .17 .358

Line 3 7 5 .032 .161 .306

Line 4 5 4 .01 .085 .176

Line 5 6 4 .017 .092 0

Table A.3: Two winding transformer data

Two

Winding

Transformer

From Bus To Bus Resistance (r, p.u.) Reactance (x, p.u.)Primary and Secondary

voltage ratio (KV/KV)

2 7 0 .0625 18/230

3 9 0 .0586 13.8/230

1 4 0 .0576 16.5/230

Table A.4: PQ Load data

Parameter Symbol Load 1 Load 2 Load 3

Bus Number - 6 8 5

Power Rating Sn 100 100 100

Active Power Rating P0 .90 1 1.25

Reactive Power Rating Q0 .30 0.35 0.5

Table A.5: AVR data

Parameter Symbol AVR 1 AVR 2 AVR 3

Genrator Number - 1 2 3

Exciter Type - 2 2 2

Maximum regulator voltage vmaxr 5 5 5

Minimum regulator voltage vminr -5 -5 -5

Amplifier gain Ka 20 20 20

Amplifier time constant Ta 0.2 0.2 0.2

Stabilizer gain Kf .063 .063 .063

Stabilizer time constant Tf 0.35 0.35 0.35

Field circuit integral deviation Ke 1 1 1

Field circuit time constant Te 0.314 0.314 0.314

Measurement time constant Tr .001 .001 .001

1st ceiling coefficient Ae .0039 .0039 .0039

2nd ceiling coefficient Be 1.555 1.555 1.555

A.3.2 14-Bus Test System

The single line diagram of IEEE 14-Bus system with the complete data is given in fol-

lowing.

65


Figure A.14: IEEE 14-Bus test System [27].

Table A.6: Synchronous Generator Data of IEEE 14-Bus system

Parameter Symbol Unit Gen 1 Gen 2 Gen 3 Gen 4 Gen 5Bus Number - - 1 3 2 8 6Power rating Sn MVA 100 100 100 100 100Voltage rating Vn kV 615 69 69 25 25Frequency rating fn Hz 60 60 60 60 60Machine order - - 4 4 4 4 4Armature resitance ra p.u. 0 .0031 .0031 0.0014 0.0014d-axis synchronous reactance xd p.u. .8979 1.05 1.05 1.25 1.25d-axis transient reactance x′d p.u. .232 .1850 .1850 .232 .232d-axis sub-transient reactance x′′d p.u. 0.4 0.13 0.13 0.12 0.12d-axis open circuit transienttime constant T ′d0 s 7.4 6.1 6.1 4.75 4.75q-axis synchronous reactance xq p.u. .0969 .8645 1.2578q-axis transient reactance x′q p.u. .646 .98 .98 1.22 1.22q-axis sub-transient reactance x′′q p.u. .646 .36 .36 .715 .715q-axis open circuit transienttime constant T ′q0 s .001 .3 0.3 1.5 1.5

Mechanical starting time M = 2H kWs/kVA 10.296 13.08 13.08 10.12 10.12Damping Coefficent D - 2 2 2 2 2Speed feedback gain Kw gain 0 0 0 0 0Active power feedback gain KP gain 0 0 0 0 0

66


Table A.7: Line Data of IEEE 14-Bus System

From Bus To Bus Resistance (r, p.u.) Reactance (x, p.u.)Shunt

susceptance (b, p.u.)2 5 .05695 .17388 .3046 12 .12291 .25581 012 13 .22092 .19988 06 11 .09498 .1989 .30611 10 .08205 .19207 09 10 .03181 .0845 09 14 .12711 .27038 014 13 .17093 .34802 07 9 0 .11001 01 2 .01938 .05917 .05283 2 .04699 .19797 .04383 4 .06701 .17103 .03461 5 .05403 .22304 .04925 4 .01335 .043211 .01282 4 .05811 .17632 .0374

Table A.8: Two winding transformer data of IEEE-14 Bus system

TwoWindingTransformer

From Bus To Bus Resistance (r, p.u.) Reactance (x, p.u.)Primary and Secondaryvoltage ratio (KV/KV)

5 6 0 .25202 69/13.84 7 0 .20912 69/13.88 7 0 .17615 18/13.8

Table A.9: PQ Load data of IEEE-14 Bus system

Bus Number Power Rating ( Sn) Active Power Rating (P0 ) Reactive Power Rating (Q0)11 100 .049 .025213 100 .189 .08123 100 1.3188 .2665 100 .1064 .02242 100 .3038 .17786 100 .1568 .1054 100 .6692 .05614 100 .2086 .0712 100 .0854 .022410 100 .126 .08129 100 .413 .2324

Table A.10: AVR data

Parameter Symbol AVR 1 AVR 2 AVR 3 AVR 4 AVR 5Genrator Number - 1 3 2 4 5Exciter Type - 2 2 2 2 2Maximum regulator voltage vmax

r 7.32 4.38 4.38 6.81 6.81Minimum regulator voltage vmin

r 0 0 0 1.395 1.395Amplifier gain Ka 200 20 20 20 20Amplifier time constant Ta 0.02 0.02 0.02 0.02 0.02Stabilizer gain Kf .002 .001 .001 .001 .001Stabilizer time constant Tf 1 1 1 1 1Field circuit integral deviation Ke 1 1 1 1 1Field circuit time constant Te 0.2 1.98 1.98 0.7 0.7Measurement time constant Tr .001 .001 .001 .001 .0011st ceiling coefficient Ae .0006 .0006 .0006 .0006 .00062nd ceiling coefficient Be 0.9 0.9 0.9 0.9 0.9

67


Table A.11: ULTC (in IEEE-14 Bus) data

Parameter Symbol Unit Value Parameter Symbol Unit ValueSending end bus nominal voltage V bus1 V 69000 Inverse time constant K 1/s 0.10Receiving end bus voltage V bus2 V 13800 Max tap ratio mmax p.u./p.u. 1.20Power Rating Sn MVA 100 Min tap ratio mmin p.u./p.u. 0.8Voltage rating V n V 69000 Tap ratio step deltam p.u./p.u. 0Frequency rating fn Hz 60 Reference voltage vref p.u. 1.0129Nominal tap ratio kT KV/KV 5 Transformer Reactance xT p.u. 0.55618Integral deviation H p.u. 0.10 Transformer Resistance rT p.u. 0

Table A.12: PST (in IEEE-14 Bus) data

Parameter Symbol Unit Value Parameter Symbol Unit ValueSending end bus nominal voltage V bus1 V 69000 Proportional gain Kp - 0.05Receiving end bus voltage V bus2 V 13800 Integral gain Ki - 0.1Power Rating Sn MVA 100 Reference Power pref p.u. 0.16Primary Voltage rating V n1 V 69000 Maximum Phase angle alphamax rad pi/2Secondary voltage rating V n2 V 13800 Maximum Phase angle alphamin rad -pi/2Frequency rating fn Hz 60 Transformer Reactance xT p.u. 0.55618Measurement time constant Tm s 0.001 Transformer Resistance rT p.u. 0Fixed Tap ratio m p.u./p.u. 0.939

Table A.13: TWT (in IEEE-14 Bus) data

Parameter Symbol Unit Value Parameter Symbol Unit ValuePower Rating Sn MVA 100 Resistance of branch 1-3 R13 p.u. 0Sending end bus voltage V bus V 69000 Resistance of branch 2-3 R23 p.u. 0Voltage rating of the first winding V n1 V 69000 Reactance of branch 1-2 X12 p.u. .31193Voltage rating of the second winding V n2 V 13800 Reactance of branch 1-3 X13 p.u. .385127Voltage rating of the third winding V n3 V 18000 Reactance of branch 2-3 X23 p.u. .28616Frequency rating fn Hz 60 Fixed tap ratio m p.u./p.u. 1Resistance of branch 1-2 R12 p.u. 0

68

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